Internal problem ID [7931]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 351.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {y^{\prime } \cos \relax (y)+x \sin \relax (y) \left (\cos ^{2}\relax (y)\right )-\left (\sin ^{3}\relax (y)\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.058 (sec). Leaf size: 55
dsolve(diff(y(x),x)*cos(y(x))+x*sin(y(x))*cos(y(x))^2-sin(y(x))^3 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \arcsin \left (\frac {1}{\sqrt {1-\sqrt {\pi }\, {\mathrm e}^{x^{2}} \erf \relax (x )-2 c_{1} {\mathrm e}^{x^{2}}}}\right ) \\ y \relax (x ) = -\arcsin \left (\frac {1}{\sqrt {1-\sqrt {\pi }\, {\mathrm e}^{x^{2}} \erf \relax (x )-2 c_{1} {\mathrm e}^{x^{2}}}}\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 29.528 (sec). Leaf size: 66
DSolve[x*Cos[y[x]]^2*Sin[y[x]] - Sin[y[x]]^3 + Cos[y[x]]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\cot ^{-1}\left (\sqrt {e^{x^2} \left (-\sqrt {\pi } \text {Erf}(x)+4 c_1\right )}\right ) \\ y(x)\to \cot ^{-1}\left (\sqrt {e^{x^2} \left (-\sqrt {\pi } \text {Erf}(x)+4 c_1\right )}\right ) \\ y(x)\to 0 \\ \end{align*}